Synchronization Control Based on Sequential Convergence

Dear Editor, This letter focuses on the synchronization of system state components under the constraint of convergence sequence. Firstly, we introduce the predefined-sequence-synchronized control problem, a unique synchronization challenge where all state components must be synchronized to the origin following a predefined convergence sequence. A controller is proposed to solve the predefined-sequence-synchronized control problem in first-order affine systems, and the proposed controller can regulate the convergence sequence of state components by adjusting their ratios. Finally, the effectiveness of the theoretical findings is demonstrated through a numerical examnle.